What is the value of -e^{-0}cos(0)-e^{-0}sin(0) ?

The value of -e^{-0}cos(0)-e^{-0}sin(0) is -1

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-e^{-0}cos(0)-e^{-0}sin(0)

- e^{- 0} cos (0) - e^{- 0} sin (0)

- 1

Solution steps

- e^{- 0} cos (0) - e^{- 0} sin (0)

Use the following trivial identity:

cos (0) = 1

cos (0)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

Use the following trivial identity:

sin (0) = 0

sin (0)

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= - e^{- 0} \cdot 1 - e^{- 0} \cdot 0

Simplify

= - 1

4 sin (\frac{7 π}{4})

arccot (- \frac{1}{3})

cot (\frac{17 π}{3})

arctan (- 3)

cot (\frac{17 π}{2})

What is the value of -e^{-0}cos(0)-e^{-0}sin(0) ?
The value of -e^{-0}cos(0)-e^{-0}sin(0) is -1